Local Fitting Method Research Articles

Single-shot surface profiling by local model fitting

A new surface profiling algorithm called the local model fitting (LMF) method is proposed. LMF is a single-shot method that employs only a single image, so it is fast and robust against vibration. LMF does not require a conventional assumption of smoothness of the target surface in a band-limit sense, but we instead assume that the target surface is locally constant. This enables us to recover sharp edges on the surface. LMF employs only local image data, so objects covered with heterogeneous materials can also be measured. The LMF algorithm is simple to implement and is efficient in computation. Experimental results showed that the proposed LMF method works very well.

Ab initio quantum dynamics study of rotationally inelastic scattering of glycine by hydrogen atom

Quantum mechanical study has been carried out to investigate rotationally inelastic scattering of glycine by a hydrogen atom. In this study, the glycine is treated as a rigid body fixed in an equilibrium geometry, which results in a three-dimensional quantum scattering problem. In our study, ab initio calculations are first performed to generate potential energies in a three-dimensional (3-D) grid. These discrete energy points are used to fit into a 3-D potential energy surface using a local fitting method to generate potential energies at any given point in 3-D space. Time-dependent quantum dynamics calculation is performed to obtain state-to-state rotationally inelastic transition probabilities of glycine. The individual transition probabilities exhibit oscillatory behavior and have similar magnitude on the order of a few percent. Overall, the energy transfer between translation and rotation is generally small due to the smallness of the rotation constant of glycine.

Comparison of Some Neural Network and Scattered Data Approximations: The Inverse Manipulator Kinematics Example

This paper compares the application of five different methods for the approximation of the inverse kinematics of a manipulator arm from a number of joint angle/Cartesian coordinate training pairs. The first method is a standard feedforward neural network with error backpropagation learning. The next two methods are derived from an extended Kohonen Map algorithm that we combine with Shepard interpolation for the forward computation. We compare the method of Ritter et al. for the learning of the extended Kohonen Map to our own scheme based on gradient descent optimization. We also study three scattered data approximation algorithms. They include two variants of the Radial Basis Function (RBF) method: Hardy's multiquadrics and gaussian RBF. We further develop our own Local Polynomial Fit method that could be considered as a modification of McLain's method. We propose extensions to the considered scattered data approximation algorithms to make them suitable for vector-valued multivariable functions, such as the mapping of Cartesian coordinates into joint angle coordinates.